RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_02:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.81 14.4982 0.368427
2 to 25 15.52 21.8582 0.809765
3 to 26 15.90 17.8904 0.604215
4 to 27 15.80 17.8506 0.601674
5 to 28 15.64 18.3306 0.631721
6 to 29 15.82 16.6128 0.519116
7 to 30 15.56 17.5204 0.580315
8 to 31 15.66 20.3977 0.745608
9 to 32 15.86 16.1970 0.490084
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.125185
Tough bday spacings test for dh-ranFile-2018-07-05_02:31: 4096 birthdays, year=2^32 days
Table of Expected vs. Observed counts:
Duplicates 0 1 2 3 4 5 6 7 8 9 >=10
Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1
Observed 2 34 82 106 95 73 63 26 7 7 5
(O-E)^2/E 5.6 0.2 1.0 0.7 0.1 0.3 2.3 0.5 4.2 0.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 15.119, p= 0.872
RESULTS OF GCD FOR dh-ranFile-2018-07-05_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.023337
p-value, dist. of gcd's: 0.204087
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.215 0.664 0.903 0.398 0.042 0.552 0.888 0.175
Bits 8 to 15---> 0.977 0.948 0.408 0.909 0.725 0.931 0.708 0.226
Bits 16 to 23---> 0.562 0.175 0.075 0.302 0.993 0.058 0.385 0.292
Bits 24 to 31---> 0.611 0.145 0.978 0.490 0.155 0.180 0.321 0.506
KS test for the above 32 p values: 0.490
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_02:31,
p-values for 5 runs: 0.7457, 0.0981, 0.8079, 0.6611, 0.0749
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 231 211.4 1.814 1.814
r= 29 5088 5134.0 0.412 2.226
r= 30 23127 23103.0 0.025 2.251
r= 31 11554 11551.5 0.001 2.251
chi-square = 2.251 with df = 3; p-value = 0.478
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 213 211.4 0.012 0.012
r= 30 5111 5134.0 0.103 0.115
r= 31 23094 23103.0 0.004 0.119
r= 32 11582 11551.5 0.080 0.199
chi-square = 0.199 with df = 3; p-value = 0.022
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_02:31
b-rank test for bits 1 to 8, p=0.46913
b-rank test for bits 2 to 9, p=0.42451
b-rank test for bits 3 to 10, p=0.77956
b-rank test for bits 4 to 11, p=0.99001
b-rank test for bits 5 to 12, p=0.96039
b-rank test for bits 6 to 13, p=0.65335
b-rank test for bits 7 to 14, p=0.77633
b-rank test for bits 8 to 15, p=0.21199
b-rank test for bits 9 to 16, p=0.90518
b-rank test for bits 10 to 17, p=0.38279
b-rank test for bits 11 to 18, p=0.38528
b-rank test for bits 12 to 19, p=0.26273
b-rank test for bits 13 to 20, p=0.72298
b-rank test for bits 14 to 21, p=0.02683
b-rank test for bits 15 to 22, p=0.24600
b-rank test for bits 16 to 23, p=0.47872
b-rank test for bits 17 to 24, p=0.69952
b-rank test for bits 18 to 25, p=0.70817
b-rank test for bits 19 to 26, p=0.88893
b-rank test for bits 20 to 27, p=0.65851
b-rank test for bits 21 to 28, p=0.02014
b-rank test for bits 22 to 29, p=0.55107
b-rank test for bits 23 to 30, p=0.52325
b-rank test for bits 24 to 31, p=0.55797
b-rank test for bits 25 to 32, p=0.42933
TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices
The above should be 25 uniform [0,1] random variables:
The KS test for those 25 supposed UNI's yields p = 0.556505
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_02:31
(20 bits/word, 2097152 words 20 bitstreams. No. missing words
should average 141909.33 with sigma=428.00.)
----------------------------------------------------------------
BITSTREAM test results.
Bitstream No. missing words z-score p-value
1 142112 0.47 0.682082
2 142209 0.70 0.758087
3 141896 -0.03 0.487577
4 142375 1.09 0.861706
5 142307 0.93 0.823591
6 142167 0.60 0.726424
7 141781 -0.30 0.382151
8 142148 0.56 0.711455
9 142430 1.22 0.888106
10 141365 -1.27 0.101722
11 141539 -0.87 0.193449
12 141837 -0.17 0.432900
13 142313 0.94 0.827199
14 142069 0.37 0.645448
15 141745 -0.38 0.350508
16 141315 -1.39 0.082474
17 141541 -0.86 0.194734
18 142046 0.32 0.625259
19 142216 0.72 0.763164
20 141368 -1.26 0.102973
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_02:31
Bits used No. missing words z-score p-value
23 to 32 141716 -0.6667 0.252496
22 to 31 141412 -1.7149 0.043179
21 to 30 142001 0.3161 0.624038
20 to 29 141792 -0.4046 0.342891
19 to 28 142104 0.6713 0.748978
18 to 27 142284 1.2920 0.901815
17 to 26 142240 1.1402 0.872907
16 to 25 141756 -0.5287 0.298498
15 to 24 141819 -0.3115 0.377717
14 to 23 141438 -1.6253 0.052052
13 to 22 141971 0.2127 0.584202
12 to 21 141828 -0.2804 0.389567
11 to 20 141918 0.0299 0.511925
10 to 19 141460 -1.5494 0.060641
9 to 18 142240 1.1402 0.872907
8 to 17 142212 1.0437 0.851686
7 to 16 141864 -0.1563 0.437894
6 to 15 141982 0.2506 0.598933
5 to 14 141544 -1.2598 0.103878
4 to 13 142095 0.6402 0.738992
3 to 12 142256 1.1954 0.884037
2 to 11 141690 -0.7563 0.224732
1 to 10 142180 0.9333 0.824679
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_02:31
Bits used No. missing words z-score p-value
28 to 32 141848 -0.2079 0.417654
27 to 31 142111 0.6836 0.752895
26 to 30 142152 0.8226 0.794635
25 to 29 142368 1.5548 0.940005
24 to 28 141441 -1.5876 0.056193
23 to 27 142185 0.9345 0.824970
22 to 26 141702 -0.7028 0.241086
21 to 25 142227 1.0768 0.859226
20 to 24 141264 -2.1876 0.014351
19 to 23 141822 -0.2960 0.383602
18 to 22 141534 -1.2723 0.101632
17 to 21 141699 -0.7130 0.237928
16 to 20 141689 -0.7469 0.227568
15 to 19 142197 0.9752 0.835258
14 to 18 141956 0.1582 0.562852
13 to 17 141689 -0.7469 0.227568
12 to 16 141673 -0.8011 0.211532
11 to 15 141614 -1.0011 0.158385
10 to 14 141895 -0.0486 0.480629
9 to 13 141810 -0.3367 0.368167
8 to 12 142085 0.5955 0.724243
7 to 11 142231 1.0904 0.862233
6 to 10 141598 -1.0554 0.145631
5 to 9 141872 -0.1265 0.449651
4 to 8 142128 0.7413 0.770730
3 to 7 141922 0.0429 0.517129
2 to 6 142064 0.5243 0.699967
1 to 5 142250 1.1548 0.875917
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_02:31
Bits used No. missing words z-score p-value
31 to 32 141205 -2.0777 0.018870
30 to 31 141756 -0.4523 0.325526
29 to 30 141933 0.0698 0.527833
28 to 29 142158 0.7335 0.768385
27 to 28 141554 -1.0482 0.147280
26 to 27 141567 -1.0098 0.156290
25 to 26 142140 0.6804 0.751888
24 to 25 142052 0.4209 0.663070
23 to 24 141529 -1.1219 0.130949
22 to 23 141951 0.1229 0.548915
21 to 22 141978 0.2026 0.580263
20 to 21 142050 0.4150 0.660913
19 to 20 142013 0.3058 0.620126
18 to 19 141898 -0.0334 0.486669
17 to 18 141997 0.2586 0.602033
16 to 17 141703 -0.6086 0.271381
15 to 16 142251 1.0079 0.843243
14 to 15 141633 -0.8151 0.207498
13 to 14 141509 -1.1809 0.118818
12 to 13 142086 0.5212 0.698869
11 to 12 142001 0.2704 0.606579
10 to 11 142475 1.6686 0.952406
9 to 10 142414 1.4887 0.931717
8 to 9 141957 0.1406 0.555915
7 to 8 141985 0.2232 0.588316
6 to 7 141886 -0.0688 0.472566
5 to 6 141980 0.2085 0.582568
4 to 5 141414 -1.4612 0.071987
3 to 4 141929 0.0580 0.523135
2 to 3 142280 1.0934 0.862896
1 to 2 142342 1.2763 0.899078
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2540.19 0.568 0.715101
Test results for specific bytes for dh-ranFile-2018-07-05_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2489.68 -0.146 0.441976
2 to 9 2515.97 0.226 0.589335
3 to 10 2686.68 2.640 0.995856
4 to 11 2357.51 -2.015 0.021943
5 to 12 2560.86 0.861 0.805292
6 to 13 2433.28 -0.943 0.172713
7 to 14 2527.08 0.383 0.649141
8 to 15 2490.68 -0.132 0.447548
9 to 16 2496.22 -0.054 0.478657
10 to 17 2556.58 0.800 0.788184
11 to 18 2540.57 0.574 0.716907
12 to 19 2438.74 -0.866 0.193145
13 to 20 2644.61 2.045 0.979579
14 to 21 2458.48 -0.587 0.278531
15 to 22 2555.90 0.791 0.785412
16 to 23 2362.46 -1.945 0.025884
17 to 24 2470.68 -0.415 0.339202
18 to 25 2497.19 -0.040 0.484174
19 to 26 2451.71 -0.683 0.247329
20 to 27 2417.16 -1.171 0.120701
21 to 28 2529.87 0.422 0.663623
22 to 29 2500.95 0.013 0.505342
23 to 30 2402.66 -1.377 0.084311
24 to 31 2505.91 0.084 0.533283
25 to 32 2418.31 -1.155 0.123991
CDPARK for dh-ranFile-2018-07-05_02:31: result of 10 tests
(Of 12000 tries, the average no. of successes should be
3523.0 with sigma=21.9)
No. succeses z-score p-value
3540 0.7763 0.781201
3550 1.2329 0.891189
3517 -0.2740 0.392053
3524 0.0457 0.518210
3549 1.1872 0.882429
3550 1.2329 0.891189
3550 1.2329 0.891189
3524 0.0457 0.518210
3493 -1.3699 0.085365
3519 -0.1826 0.427537
Square side=100, avg. no. parked=3531.60 sample std.=18.35
p-value of the KSTEST for those 10 p-values: 0.178109
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_02:31
0.7895,0.6931,0.8677,0.5707,0.4298,0.5795,0.3900,0.1489,0.1217,0.5784,
The KS test for those 10 p-values: 0.799927
The 3DSPHERES test for dh-ranFile-2018-07-05_02:31
sample no r^3 equiv. uni.
1 4.946 0.152001
2 20.691 0.498281
3 6.745 0.201349
4 25.127 0.567242
5 12.177 0.333630
6 15.590 0.405274
7 13.716 0.366939
8 2.802 0.089175
9 35.774 0.696525
10 28.226 0.609709
11 57.588 0.853334
12 137.969 0.989938
13 12.403 0.338625
14 66.227 0.890032
15 26.598 0.587948
16 16.650 0.425928
17 35.169 0.690341
18 44.970 0.776648
19 32.080 0.656758
20 54.180 0.835692
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.653576
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.1 -1.3 0.9 1.6 0.4
-0.5 -0.1 0.7 -0.3 -0.6 -0.1
-1.8 0.6 0.6 -0.0 0.6 1.0
1.6 -1.5 0.5 -1.3 -0.2 0.1
-0.4 1.2 -1.0 -0.6 -0.6 -1.2
0.5 0.9 1.2 -0.3 -0.5 0.4
-1.6 -1.0 0.5 -0.7 -1.3 -1.0
-0.1
Chi-square with 42 degrees of freedom:35.436739
z-score=-0.716111, p-value=0.247171
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_02:31
Test no p-value
1 0.878733
2 0.273243
3 0.311419
4 0.294960
5 0.201540
6 0.014297
7 0.898381
8 0.718724
9 0.361438
10 0.138896
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.405609
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_02:31:
(for k>=2, the prob. of a run of length k is 2*k/(k+1)!)
Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E
2 66666.67 66841 0.46 66795 0.25
3 25000.00 24765 2.21 24854 0.85
4 6666.67 6694 0.11 6616 0.39
5 1388.89 1425 0.94 1443 2.11
6 238.10 222 1.09 246 0.26
7 34.72 45 3.04 38 0.31
8 4.96 7 0.84 7 0.84
p=0.80801 p=0.45673
Number of rngs required: 688761, p-value: 0.660
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_02:31
No. of wins: Observed Expected
98561 98585.9
z-score=-0.111, pvalue=0.45574
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66896 66666.7 0.789 0.789
2 37325 37654.3 2.880 3.669
3 26981 26954.7 0.026 3.695
4 19376 19313.5 0.203 3.897
5 13859 13851.4 0.004 3.901
6 9951 9943.5 0.006 3.907
7 7130 7145.0 0.032 3.939
8 5230 5139.1 1.609 5.547
9 3759 3699.9 0.945 6.493
10 2536 2666.3 6.367 12.860
11 1908 1923.3 0.122 12.982
12 1404 1388.7 0.168 13.150
13 988 1003.7 0.246 13.396
14 698 726.1 1.091 14.486
15 524 525.8 0.006 14.493
16 373 381.2 0.174 14.667
17 303 276.5 2.532 17.199
18 203 200.8 0.023 17.222
19 147 146.0 0.007 17.229
20 119 106.2 1.539 18.768
21 290 287.1 0.029 18.797
Chisq= 18.80 for 20 degrees of freedom, p= 0.46497
SUMMARY of craptest
p-value for no. of wins: 0.455736
p-value for throws/game: 0.464968
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_02:31
No. of wins: Observed Expected
98773 98585.9
z-score= 0.837, pvalue=0.79871
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67013 66666.7 1.799 1.799
2 37784 37654.3 0.447 2.246
3 26667 26954.7 3.071 5.317
4 19191 19313.5 0.777 6.094
5 13905 13851.4 0.207 6.301
6 9985 9943.5 0.173 6.474
7 7125 7145.0 0.056 6.530
8 5082 5139.1 0.634 7.164
9 3631 3699.9 1.282 8.446
10 2627 2666.3 0.579 9.025
11 2004 1923.3 3.384 12.408
12 1351 1388.7 1.026 13.434
13 982 1003.7 0.470 13.904
14 720 726.1 0.052 13.956
15 524 525.8 0.006 13.962
16 357 381.2 1.530 15.492
17 283 276.5 0.151 15.643
18 214 200.8 0.864 16.507
19 128 146.0 2.216 18.723
20 111 106.2 0.216 18.938
21 316 287.1 2.906 21.844
Chisq= 21.84 for 20 degrees of freedom, p= 0.65098
SUMMARY of craptest
p-value for no. of wins: 0.798705
p-value for throws/game: 0.650979
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0143,0.0144,0.0189,0.0201,0.0219,0.0222,0.0233,0.0259,0.0268,0.0423,
0.0432,0.0521,0.0562,0.0582,0.0606,0.0720,0.0748,0.0749,0.0825,0.0843,
0.0854,0.0892,0.0981,0.1016,0.1017,0.1030,0.1039,0.1188,0.1207,0.1217,
0.1240,0.1252,0.1309,0.1389,0.1453,0.1456,0.1473,0.1489,0.1520,0.1547,
0.1563,0.1584,0.1727,0.1749,0.1753,0.1781,0.1797,0.1931,0.1934,0.1947,
0.2013,0.2015,0.2041,0.2075,0.2115,0.2120,0.2154,0.2247,0.2257,0.2276,
0.2276,0.2379,0.2411,0.2460,0.2472,0.2473,0.2525,0.2627,0.2714,0.2732,
0.2785,0.2922,0.2950,0.2985,0.3024,0.3114,0.3207,0.3255,0.3336,0.3386,
0.3392,0.3429,0.3505,0.3614,0.3669,0.3682,0.3684,0.3777,0.3822,0.3828,
0.3836,0.3850,0.3853,0.3896,0.3900,0.3921,0.3976,0.4053,0.4056,0.4076,
0.4177,0.4245,0.4259,0.4275,0.4293,0.4298,0.4329,0.4379,0.4420,0.4475,
0.4497,0.4557,0.4567,0.4650,0.4691,0.4726,0.4781,0.4787,0.4787,0.4806,
0.4842,0.4867,0.4876,0.4897,0.4897,0.4901,0.4983,0.5053,0.5058,0.5119,
0.5171,0.5182,0.5182,0.5191,0.5231,0.5232,0.5278,0.5333,0.5489,0.5511,
0.5521,0.5559,0.5565,0.5580,0.5616,0.5629,0.5672,0.5707,0.5784,0.5795,
0.5803,0.5803,0.5826,0.5842,0.5879,0.5883,0.5893,0.5989,0.6017,0.6020,
0.6042,0.6066,0.6097,0.6112,0.6201,0.6240,0.6253,0.6317,0.6454,0.6491,
0.6510,0.6534,0.6536,0.6568,0.6585,0.6599,0.6609,0.6611,0.6631,0.6636,
0.6639,0.6821,0.6903,0.6931,0.6965,0.6989,0.6995,0.7000,0.7082,0.7083,
0.7115,0.7151,0.7169,0.7187,0.7230,0.7242,0.7245,0.7264,0.7390,0.7456,
0.7457,0.7490,0.7519,0.7529,0.7581,0.7632,0.7684,0.7707,0.7763,0.7766,
0.7796,0.7812,0.7854,0.7882,0.7895,0.7946,0.7987,0.7999,0.8053,0.8079,
0.8080,0.8098,0.8236,0.8247,0.8250,0.8272,0.8353,0.8357,0.8432,0.8517,
0.8533,0.8592,0.8617,0.8622,0.8629,0.8677,0.8722,0.8729,0.8729,0.8759,
0.8787,0.8824,0.8840,0.8877,0.8881,0.8889,0.8900,0.8912,0.8912,0.8912,
0.8984,0.8991,0.9018,0.9033,0.9052,0.9089,0.9307,0.9317,0.9400,0.9483,
0.9524,0.9604,0.9772,0.9779,0.9796,0.9899,0.9900,0.9934,0.9959,
Overall p-value after applying KStest on 269 p-values = 0.464215
In response to requests, we have provided a list of all the p-values
produced by the tests you have chosen for this run. The individual
p-values are supposed to be uniform in [0,1), but they are not necessarily
independent. So even though we have applied a KSTEST to the accumulated
p-values, the result is not necessarily---even if your file contains truly
random bits---uniform in [0,1). But it is probably pretty close, so take
that last p-value with a grain of salt. In particular, there may be some
values so close to 0 or 1 that the tests they came from should be applied
several more times, or new, related tests should be undertaken.